English

Let A = {A, B, C, D} And F : A → a Be Given by F = {( A,B ),( B , D ),( C , a ) , ( D , C )} Write F .

Advertisements
Advertisements

Question

Let A = {abcd} and f : A → A be given by f = {( a,b ),( b , d ),( c , a ) , ( d , c )} write `f^-1`. [NCERT EXEMPLAR]

Sum
Advertisements

Solution

We have , 

A = {a, b, c, d} and f : A 

→ A be given by f = {(a, b), (b, d), (c, a), (d, c)}

Since, the elements of a function when interchanged gives inverse function.

so, f -1 = {(b, a), (d, b), (a, c), (c, d)}

shaalaa.com
  Is there an error in this question or solution?
Chapter 2: Functions - Exercise 2.5 [Page 74]

APPEARS IN

R.D. Sharma Mathematics Volume 1 and 2 [English] Class 12
Chapter 2 Functions
Exercise 2.5 | Q 41 | Page 74

RELATED QUESTIONS

Which of the following functions from A to B are one-one and onto?

 f2 = {(2, a), (3, b), (4, c)} ; A = {2, 3, 4}, B = {abc}


Classify the following function as injection, surjection or bijection :

f : R → R, defined by f(x) = x3 + 1


Classify the following function as injection, surjection or bijection :

 f : R → R, defined by f(x) = x3 − x


Let A = [-1, 1]. Then, discuss whether the following function from A to itself is one-one, onto or bijective : g(x) = |x|  


Find gof and fog when f : R → R and g : R → R is defined by  f(x) = 2x + x2 and  g(x) = x3


Find gof and fog when f : R → R and g : R → R is defined by  f(x) = x2 + 2x − 3 and  g(x) = 3x − 4 .


Let f = {(1, −1), (4, −2), (9, −3), (16, 4)} and g = {(−1, −2), (−2, −4), (−3, −6), (4, 8)}. Show that gof is defined while fog is not defined. Also, find gof.


Let R+ be the set of all non-negative real numbers. If f : R+ → R+ and g : R+ → R+ are defined as `f(x)=x^2` and `g(x)=+sqrtx` , find fog and gof. Are they equal functions ?


Give examples of two functions f : N → Z and g : Z → Z, such that gof is injective but gis not injective.


Find fog and gof  if : f (x) = |x|, g (x) = sin x .


Find fog and gof  if : f (x) = x+1, g(x) = `e^x`

.


Find fog and gof  if : f (x) = x+1, g (x) = sin x .


Find fog and gof  if : f(x) = c, c ∈ R, g(x) = sin `x^2`


Let f(x) = x2 + x + 1 and g(x) = sin x. Show that fog ≠ gof.


If f(x) = |x|, prove that fof = f.


If f(x) = 2x + 5 and g(x) = x2 + 1 be two real functions, then describe each of the following functions:
(1) fog
(2) gof
(3) fof
(4) f2
Also, show that fof ≠ f2


Let

f (x) =`{ (1 + x, 0≤ x ≤ 2) , (3 -x , 2 < x ≤ 3):}`

Find fof.


A function f : R → R is defined as f(x) = x3 + 4. Is it a bijection or not? In case it is a bijection, find f−1 (3).


If f : R → R is defined by f(x) = x2, write f−1 (25)


Write whether f : R → R, given by `f(x) = x + sqrtx^2` is one-one, many-one, onto or into.


If f : {5, 6} → {2, 3} and g : {2, 3} → {5, 6} are given by f = {(5, 2), (6, 3)} and g = {(2, 5), (3, 6)}, then find fog.    [NCERT EXEMPLAR]


Let fg : R → R be defined by f(x) = 2x + l and g(x) = x2−2 for all x

∈ R, respectively. Then, find gof.  [NCERT EXEMPLAR]


Let 

\[A = \left\{ x \in R : - 1 \leq x \leq 1 \right\} = B\] Then, the mapping\[f : A \to \text{B given by} f\left( x \right) = x\left| x \right|\] is 

 


The function \[f : R \to R\] defined by

\[f\left( x \right) = 6^x + 6^{|x|}\] is 

 


 Let
\[g\left( x \right) = 1 + x - \left[ x \right] \text{and} f\left( x \right) = \begin{cases}- 1, & x < 0 \\ 0, & x = 0, \\ 1, & x > 0\end{cases}\] where [x] denotes the greatest integer less than or equal to x. Then for all \[x, f \left( g \left( x \right) \right)\] is equal to


If  \[f : R \to \left( - 1, 1 \right)\] is defined by

\[f\left( x \right) = \frac{- x|x|}{1 + x^2}, \text{ then } f^{- 1} \left( x \right)\] equals

 


Mark the correct alternative in the following question:
If the set A contains 7 elements and the set B contains 10 elements, then the number one-one functions from A to B is


Let the function f: R → R be defined by f(x) = 4x – 1, ∀ x ∈ R. Then, show that f is one-one.


Let f: R → R be defined by f(x) = 3x – 4. Then f–1(x) is given by ______.


Let f: R → R be the functions defined by f(x) = x3 + 5. Then f–1(x) is ______.


If f(x) = (4 – (x – 7)3}, then f–1(x) = ______.


The function f : A → B defined by f(x) = 4x + 7, x ∈ R is ____________.


Let f : R `->` R be a function defined by f(x) = x3 + 4, then f is ______.


Let n(A) = 4 and n(B) = 6, Then the number of one – one functions from 'A' to 'B' is:


Let the function f: R → R be defined by f(x) = 4x – 1, ∀ x ∈ R then 'f' is


Prove that the function f is surjective, where f: N → N such that `f(n) = {{:((n + 1)/2",", if "n is odd"),(n/2",", if  "n is even"):}` Is the function injective? Justify your answer.


Let S = {1, 2, 3, 4, 5, 6, 7}. Then the number of possible functions f: S `rightarrow` S such that f(m.n) = f(m).f(n) for every m, n ∈ S and m.n ∈ S is equal to ______.


The trigonometric equation tan–1x = 3tan–1 a has solution for ______.



The given function f : R → R is not ‘onto’ function. Give reason.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×